Question

A spherical marble of mass m is projected horizontally through a fluid

that exerts a linear resistive force of the form f(v) = −bv. [i.e. the minus sign indicates the force acts opposite to

the velocity so f⃗= −bvû. ] Ignore all other forces on the marble (e.g. by putting it on horizontal frictionless t

track), and treat the motion as one-dimensional along the x axis. The marble is launched at x = 0 with initial velocity v₀. Find:
a) v(t) by separating variables;
b) x(t).

c) Show v(x) is a linear function in x using either a(v)dx = vdv and separating variables, or using (a)/(b).

[ d(ln(z))/dz = 1/z , d(ez)/dz = ez.]

Answer 1

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